DocumentCode :
941004
Title :
On nonparametric estimation of a functional of a probability density
Author :
Pawlak, Miroslaw
Volume :
32
Issue :
1
fYear :
1986
fDate :
1/1/1986 12:00:00 AM
Firstpage :
79
Lastpage :
84
Abstract :
The nonparametric estimate derived from the Hermite orthogonal system of the functional 
where 
is an unknown probability density, is studied. Sufficient conditions for the weak and strong consistency of the estimate are presented, and the rate of convergence is given. In particular, under mild assumptions on , the rate of mean-square error convergence is 
, whereas for almost complete convergence it is 
. Moreover, several possible applications in the area of nonparametric inference of the estimate are indicated.
where is an unknown probability density, is studied. Sufficient conditions for the weak and strong consistency of the estimate are presented, and the rate of convergence is given. In particular, under mild assumptions on , the rate of mean-square error convergence is , whereas for almost complete convergence it is . Moreover, several possible applications in the area of nonparametric inference of the estimate are indicated.Keywords :
Estimation; Probability; Convergence; Distribution functions; Kernel; Random variables; Signal detection; Statistical analysis; Statistical distributions; Statistics; Sufficient conditions; Testing;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1986.1057120
Filename :
1057120
Link To Document :
